IEEE Transactions on Information Theory最新文献

{"title":"Quantum X-Secure E-Eavesdropped T-Colluding Symmetric Private Information Retrieval","authors":"Alptug Aytekin;Mohamed Nomeir;Sajani Vithana;Sennur Ulukus","doi":"10.1109/TIT.2025.3551697","DOIUrl":"https://doi.org/10.1109/TIT.2025.3551697","url":null,"abstract":"We consider both classical and quantum variations of <italic>X</i>-secure, <italic>E</i>-eavesdropped and <italic>T</i>-colluding symmetric private information retrieval (SPIR). This is the first work to study SPIR with <italic>X</i>-security in classical or quantum variations. We first develop a scheme for classical <italic>X</i>-secure, <italic>E</i>-eavesdropped and <italic>T</i>-colluding SPIR (XSETSPIR) based on a modified version of cross subspace alignment (CSA), which achieves a rate of <inline-formula> <tex-math>$R= 1 - frac {X+max (T,E)}{N}$ </tex-math></inline-formula>. The modified scheme achieves the same rate as the scheme used for <italic>X</i>-secure PIR with the extra benefit of symmetric privacy, i.e., user-privacy as well as database-privacy. Next, we extend this scheme to its quantum counterpart based on the <italic>N</i>-sum box abstraction. This is the first work to consider the presence of eavesdroppers in quantum private information retrieval (QPIR). In the quantum variation, the eavesdroppers have better access to information over the quantum channel compared to the classical channel due to the over-the-air decodability. To that end, we develop two different schemes for quantum <italic>X</i>-secure, <italic>E</i>-eavesdropped and <italic>T</i>-colluding SPIR (QXSETSPIR) with secure over-the-air decoding. The first scheme achieves the highest possible super-dense coding gain, i.e., <inline-formula> <tex-math>$R_{Q} = min left {{{ 1, 2left ({{1-frac {X+max (T,E)}{N}}}right)}}right }$ </tex-math></inline-formula>, which requires additional uploads from the user. The second scheme on the other hand requires no extra uploads. However, it does not achieve the super-dense coding gain in some cases based on the relation between the number of eavesdropped links and the number of interference terms. The second scheme is based on the idea that there exist some special entanglement states that can be used to hide the contents of the user-required messages from the eavesdroppers using the interference symbols.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 5","pages":"3974-3988"},"PeriodicalIF":2.2,"publicationDate":"2025-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143870962","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Globally-Optimal Greedy Active Sequential Estimation","authors":"Xiaoou Li;Hongru Zhao","doi":"10.1109/TIT.2025.3551621","DOIUrl":"https://doi.org/10.1109/TIT.2025.3551621","url":null,"abstract":"Motivated by modern applications such as computerized adaptive testing, sequential rank aggregation, and heterogeneous data source selection, we study the problem of active sequential estimation. The goal is to design an adaptive experiment selection rule and an estimator for more accurate parameter estimation. Greedy information-based experiment selection rules, which optimize information gain one step ahead, have been employed in practice thanks to their computational convenience, flexibility to context or task changes, and broad applicability. However, the optimality of greedy methods under a sequential decision theory framework is only established in the one-dimensional case, partly due to the problem’s combinatorial nature and the seemingly limited capacity of greedy algorithms. In this study, we close the gap for multidimensional problems. We cast the problem under a sequential decision theory framework with generalized risk measures for a large class of design-and-estimation methods. We propose adopting the maximum likelihood estimator with a class of greedy experiment selection rules. This class encompasses both existing methods and introduces new methods with improved numerical efficiency. We prove that these methods achieve asymptotic optimality when the risk measure aligns with the selection rule. Additionally, we establish that the proposed estimators are consistent and asymptotically normal, and further extend the results to allow early stopping rules. We also perform extensive numerical studies on both simulated and real data to illustrate the efficacy of the proposed methods.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 5","pages":"3871-3924"},"PeriodicalIF":2.2,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143870927","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Level Crossing Rate Inequalities for Product Processes and Applications to Fading Multichannels","authors":"Plínio Santini Dester;Michel Daoud Yacoub;Paulo Cardieri","doi":"10.1109/TIT.2025.3551321","DOIUrl":"https://doi.org/10.1109/TIT.2025.3551321","url":null,"abstract":"This paper presents <italic>sharp</i> inequalities for the level crossing rate of a stochastic process composed of the product of independent stochastic processes. The inequalities, which are simple to state, enlighten the contribution of each process individually. Additionally, we derive an exact formulation when the conditioned pointwise derivative of each process follows a Gaussian distribution. As application examples, the results are exercised in different scenarios using the <inline-formula> <tex-math>$alphatext{-}mu $ </tex-math></inline-formula> and <inline-formula> <tex-math>$kappatext{-}mu$ </tex-math></inline-formula> fading models, which encompass several other well-known models such as Semi-Gaussian, Rayleigh, Rice, Nakagami-<italic>m</i>, and Weibull. We provide unprecedented closed-form formulations for the level crossing rate bounds of the product of these widely-known fading processes. Notably, there are no closed forms for the level crossing rate of these products. Therefore, our bounds supply a benchmark for this metric, with one of them serving as an excellent approximation of the exact metric.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 5","pages":"3666-3674"},"PeriodicalIF":2.2,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143870966","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the MacWilliams Theorem Over Codes and Lattices","authors":"Zhiyong Zheng;Fengxia Liu;Kun Tian","doi":"10.1109/TIT.2025.3550982","DOIUrl":"https://doi.org/10.1109/TIT.2025.3550982","url":null,"abstract":"Analogies between codes and lattices have been extensively studied for the last decades. In this context, the MacWilliams identity is the finite analog of the Jacobi-Poisson summation formula of the theta function. Motivated by the random lattice theory, the statistical significance of MacWilliams theorem is considered. Indeed, the MacWilliams distribution provides a finite analog of the classical Gauss distribution. In particular, the MacWilliams distribution over quotient space of a code is statistically close to the uniform distribution. In the context of lattices, the analogy of MacWilliams identity associated with nu-function was conjectured by Solé in 1995. We give an answer to this problem.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 5","pages":"3560-3568"},"PeriodicalIF":2.2,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143875186","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Faster List Decoding of AG Codes","authors":"Peter Beelen;Vincent Neiger","doi":"10.1109/TIT.2025.3550750","DOIUrl":"https://doi.org/10.1109/TIT.2025.3550750","url":null,"abstract":"In this article, we present a fast algorithm performing an instance of the Guruswami-Sudan list decoder for algebraic geometry codes. We show that any such code can be decoded in <inline-formula> <tex-math>$tilde {mathcal {O}} (s^{2}ell ^{omega -1}mu ^{omega -1}(n+g) + ell ^{omega } mu ^{omega })$ </tex-math></inline-formula> operations in the underlying finite field, where <italic>n</i> is the code length, <italic>g</i> is the genus of the function field used to construct the code, <italic>s</i> is the multiplicity parameter, <inline-formula> <tex-math>$ell $ </tex-math></inline-formula> is the designed list size and <inline-formula> <tex-math>$mu $ </tex-math></inline-formula> is the smallest positive element in the Weierstrass semigroup of some chosen place.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 5","pages":"3397-3408"},"PeriodicalIF":2.2,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143875156","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Optimal Linear Codes With Few Weights From Simplicial Complexes","authors":"Bing Chen;Yunge Xu;Zhao Hu;Nian Li;Xiangyong Zeng","doi":"10.1109/TIT.2025.3550182","DOIUrl":"https://doi.org/10.1109/TIT.2025.3550182","url":null,"abstract":"Recently, constructions of optimal linear codes from simplicial complexes have attracted much attention and some related nice works were presented. Let q be a prime power. In this paper, by using the simplicial complexes of <inline-formula> <tex-math>${mathbb {F}}_{q}^{m}$ </tex-math></inline-formula> with one single maximal element, we construct four families of linear codes over the ring <inline-formula> <tex-math>${mathbb {F}}_{q}+u{mathbb {F}}_{q}$ </tex-math></inline-formula> (<inline-formula> <tex-math>$u^{2}=0$ </tex-math></inline-formula>), which generalizes the results of Wu et al. (2020). The parameters and Lee weight distributions of these four families of codes are completely determined. Most notably, via the Gray map, we obtain several classes of optimal linear codes over <inline-formula> <tex-math>${mathbb {F}}_{q}$ </tex-math></inline-formula>, including (near) Griesmer codes and distance-optimal codes. Moreover, it is shown that most of the Gray images are minimal or self-orthogonal codes which are useful in applications.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 5","pages":"3531-3543"},"PeriodicalIF":2.2,"publicationDate":"2025-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143875080","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On Zero-Error Capacity of Graphs With One Edge","authors":"Qi Cao;Qi Chen;Baoming Bai","doi":"10.1109/TIT.2025.3547929","DOIUrl":"https://doi.org/10.1109/TIT.2025.3547929","url":null,"abstract":"In this paper, we study the zero-error capacity of channels with memory, which are represented by graphs. We provide a method to construct code for any graph with one edge, thereby determining a lower bound on its zero-error capacity. Moreover, this code can achieve zero-error capacity when the symbols in a vertex with degree one are the same. We further apply our method to the one-edge graphs representing the binary channels with two memories. There are 28 possible graphs, which can be organized into 11 categories based on their symmetries. The code constructed by our method is proved to achieve the zero-error capacity for all these graphs except for the two graphs in Case 11.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 5","pages":"3350-3359"},"PeriodicalIF":2.2,"publicationDate":"2025-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143875187","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Binary Error-Correcting Codes With Minimal Noiseless Feedback","authors":"Meghal Gupta;Venkatesan Guruswami;Rachel Yun Zhang","doi":"10.1109/TIT.2025.3545097","DOIUrl":"https://doi.org/10.1109/TIT.2025.3545097","url":null,"abstract":"In the setting of error-correcting codes with feedback, Alice wishes to communicate a k-bit message x to Bob by sending a sequence of bits over a channel while noiselessly receiving feedback from Bob. It has been long known (Berlekamp, 1964) that in this model, Bob can still correctly determine x even if <inline-formula> <tex-math>$approx frac {1}{3}$ </tex-math></inline-formula> of Alice’s bits are flipped adversarially. This improves upon the classical setting without feedback, where recovery is not possible for error fractions exceeding <inline-formula> <tex-math>$frac {1}{4}$ </tex-math></inline-formula>. In the corresponding setting of erasures rather than bit flips, feedback improves the error resilience from <inline-formula> <tex-math>$frac {1}{2}-epsilon $ </tex-math></inline-formula> to <inline-formula> <tex-math>$1-epsilon $ </tex-math></inline-formula> for any <inline-formula> <tex-math>$epsilon gt 0$ </tex-math></inline-formula>. The original feedback setting assumes that after transmitting each bit, Alice knows (via feedback) what bit Bob received. In this work, our focus in on the limited feedback model, where Bob is only allowed to send a few bits at a small number of pre-designated points in the protocol. For any desired <inline-formula> <tex-math>$epsilon gt 0$ </tex-math></inline-formula>, we construct a coding scheme that tolerates a <inline-formula> <tex-math>$ 1/3-epsilon $ </tex-math></inline-formula> fraction of bit flips (respectively a <inline-formula> <tex-math>$1-epsilon $ </tex-math></inline-formula> fraction of erasures) relying only on <inline-formula> <tex-math>$O_{epsilon } (log k)$ </tex-math></inline-formula> bits of feedback from Bob sent in a fixed <inline-formula> <tex-math>$O_{epsilon } (1)$ </tex-math></inline-formula> number of rounds. We complement this with a matching lower bound showing that <inline-formula> <tex-math>$Omega (log k)$ </tex-math></inline-formula> bits of feedback are necessary to recover from an error fraction exceeding <inline-formula> <tex-math>$1/4$ </tex-math></inline-formula> (respectively <inline-formula> <tex-math>$1/2$ </tex-math></inline-formula> for erasures), and for schemes resilient to a <inline-formula> <tex-math>$1/3-epsilon $ </tex-math></inline-formula> fraction of bit flips (respectively a <inline-formula> <tex-math>$1-epsilon $ </tex-math></inline-formula> fraction of erasures), the number of rounds must grow as <inline-formula> <tex-math>$epsilon to 0$ </tex-math></inline-formula>.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 5","pages":"3424-3446"},"PeriodicalIF":2.2,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143875081","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Strong Data Processing Inequality Under the Heat Flow","authors":"Bo'az Klartag;Or Ordentlich","doi":"10.1109/TIT.2025.3548961","DOIUrl":"https://doi.org/10.1109/TIT.2025.3548961","url":null,"abstract":"Let <inline-formula> <tex-math>$nu $ </tex-math></inline-formula> and <inline-formula> <tex-math>$mu $ </tex-math></inline-formula> be probability distributions on <inline-formula> <tex-math>$mathbb {R}^{n}$ </tex-math></inline-formula>, and <inline-formula> <tex-math>$nu _{s},mu _{s}$ </tex-math></inline-formula> be their evolution under the heat flow, that is, the probability distributions resulting from convolving their density with the density of an isotropic Gaussian random vector with variance <italic>s</i> in each entry. This paper studies the rate of decay of <inline-formula> <tex-math>$smapsto D(nu _{s}|mu _{s})$ </tex-math></inline-formula> for various divergences, including the <inline-formula> <tex-math>$chi ^{2}$ </tex-math></inline-formula> and Kullback-Leibler (KL) divergences. We prove upper and lower bounds on the strong data-processing inequality (SDPI) coefficients corresponding to the source <inline-formula> <tex-math>$mu $ </tex-math></inline-formula> and the Gaussian channel. We also prove generalizations of de Bruijn’s identity, and Costa’s result on the concavity in <italic>s</i> of the differential entropy of <inline-formula> <tex-math>$nu _{s}$ </tex-math></inline-formula>. As a byproduct of our analysis, we obtain new lower bounds on the mutual information between <italic>X</i> and <inline-formula> <tex-math>$Y=X+sqrt {s} Z$ </tex-math></inline-formula>, where <italic>Z</i> is a standard Gaussian vector in <inline-formula> <tex-math>$mathbb {R}^{n}$ </tex-math></inline-formula>, independent of <italic>X</i>, and on the minimum mean-square error (MMSE) in estimating <italic>X</i> from <italic>Y</i>, in terms of the Poincaré constant of <italic>X</i>.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 5","pages":"3317-3333"},"PeriodicalIF":2.2,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143875185","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Exponentially Consistent Outlier Hypothesis Testing for Continuous Sequences","authors":"Lina Zhu;Lin Zhou","doi":"10.1109/TIT.2025.3548918","DOIUrl":"https://doi.org/10.1109/TIT.2025.3548918","url":null,"abstract":"In outlier hypothesis testing, one aims to detect outlying sequences among a given set of sequences, where most sequences are generated i.i.d. from a nominal distribution while outlying sequences (outliers) are generated i.i.d. from a different anomalous distribution. Most existing studies focus on discrete-valued sequences, where each data sample takes values in a finite set. To account for practical scenarios where data sequences usually take real values and the number of outlying sequence is unknown, we study outlier hypothesis testing for continuous sequences when there might exist multiple outliers, and both the nominal and anomalous distributions are <italic>unknown</i>. Specifically, we propose distribution free tests and prove that the probabilities of misclassification error, false reject and false alarm decay exponentially fast for three different test designs: fixed-length test, sequential test, and two-phase test. In a fixed-length test, one fixes the sample size of each observed sequence; in a sequential test, one takes a sample sequentially from each sequence per unit time until a reliable decision can be made; in a two-phase test, one adapts the sample size from two different fixed values. Remarkably, the two-phase test achieves a good balance between test design complexity and theoretical performance.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 5","pages":"3287-3304"},"PeriodicalIF":2.2,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143875072","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}